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Probability

Short Answer Type

931. A man is known to speak the truth 5 out of 6 times. He throws a die and reports that it is a six. Find the probability that it is actually a six.

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Long Answer Type

932. Let there be three urns containing 1 white, 2 black, 3 red balls ; 2 white, 1 black, 1 red ball ; 4 white, 5 black, 3 red balls. One urn is chosen at random and two balls are drawn. These happen to be white and a red. What is the probability that they come from urn number 3.

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933. A pack of playing cards was found to contain only 51 cards. If the first 13 cards which are examined are all red, what is the probability that the missing card is black.

Let E₁ the event that the missing card is black and E₂ be the event that the missing card is red.
Let A be the event the first 13 cards which are examined are all red.
$therefore space space space space straight P left parenthesis straight E subscript 1 right parenthesis space equals space 1 half semicolon space space space space space straight P left parenthesis straight E subscript 2 right parenthesis space equals space 1 half$
P(A/E₁) = Probability of selecting 13 red cards, when the missing card is black
$equals fraction numerator space straight C presuperscript 26 subscript 13 over denominator straight C presuperscript 51 subscript 13 end fraction$
P(A/E₂) = Probability of selecting 13 red cards, when the missing card is red
$equals space fraction numerator straight C presuperscript 25 subscript 13 over denominator straight C presuperscript 51 subscript 13 end fraction$

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934.

Coloured balls are distributed in four boxes as shown in the following table:

Box		Colour
	Black	White	Red	Blue
I	3	4	5	6
II	2	2	2	2
III	1	2	3	1
IV	4	3	1	5

A box is selected at random and then a ball is randomly drawn from the selected box. The colour of the ball is black, what is the probability that ball drawn is from the box III?

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935.

Suppose we have four boxes A, B, C and D containing coloured marbles as given below:

Box	Marble Colour
	Red	White	Black
A	1	6	3
B	6	2	2
C	8	1	1
D	0	6	4

One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red. what is the probability that it was drawn from box A? box B? box C?

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Multiple Choice Questions

936. Probability that A speaks truth is

4 over 5.

A coin is tossed. A reports that a head appears. The probability that actually there was head is

$4 over 5$
$1 half$
$1 fifth$
$1 fifth$

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Short Answer Type

937. A person plays a game of tossing a coin thrice. For each head, he is given Rs. 2 by the organiser of the game and for each tail, he has to give Rs. 1.50 to the organiser. Let X denote the amount gained or lost by the person. Show that X is a random variable and exhibit it as a function on the sample space of the experiment.

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938. An urn contains 5 red and 2 black balls. Two balls are randomly drawn. Let X represent the number of black balls. What are the possible values of X ? Is X a random variable?

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939. Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed 6 times. What are possible values of X?

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940. A bag contains 2 white and 1 red balls. One ball is drawn at random and then put back in the box after noting its colour. The process is repeated again. If X denotes the number of red balls recorded in the two draws, describe X.

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